An inelastic projectile

Classical Mechanics Level 3

A small ball undergoes a partially elastic collision with a rough horizontal surface. Assume that friction $f=\mu N$ during the contact period, where $N$ is the normal reaction and $\mu$ is the coefficient of friction.

Find the value of the incoming angle $\theta$ (in degrees) such that the horizontal range of the ball after hitting the surface is maximized.

Details and Assumptions:

Take the coefficient of friction $\mu = \frac{1}{\sqrt{3}}.$
Take the coefficient of restitution $e=\sqrt{3}-1$ .

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